I'm looking at this problem which says:
Video rental for 1 day is \$1.99. Video rental for 2 days is \$2.99.
Rate of change= $\frac{2.99-1.99}{2-1}=\frac{1.00}{1}=1$
Now the problem I have with this is doesn't that mean it cost 1 dollar to rent for 1 day? However, the problem says video rental for 1 day is \$1.99.
Any ideas?
The result you got resembles the rate of change of the price per day, and that value means that the price changes 1 dollar per day, it doesn't tell you anything about the cost of rental. A simple analogy would be considering velocity, which is the rate of change of position with respect to time, the average velocity would be represented as $$v= \frac {\Delta s} {\Delta t}$$where s represents the position. Let's say you start a journey at point $a$ which is $10 km$ away from City x and continue your journey in a straight path till you reach point $b$ which is $50 km$ away from city x, and this journey takes you 100 minutes. Then your average velocity throughout the trip would be: $$v= \frac {50km-10km} {100minutes}=0.4km/min$$
Note that the $0.4km$ in the $0.4km/min$ doesn't represent your position after one minute, as you started $10km$ away from the city, however it is telling you that in $1 min$ you will be $10km + \frac {0.4km} {1minute}*1\,minute$ away from the city, or $10.4km$ away from the city. Hope this clears things up
You can say the first day is $1.99$ and the second day is $1.00$. There is no need for the days to cost the same. Maybe the third day is $5.00$ as a late return penalty. What is the problem here?